You do not mention if you have hold luggage.
Without hold luggage, providing it is not a Monday, it may be doable, as Luton a smaller airport. Make sure you have liquids already separated for scanning.
Me I would usually book an earlier coach, as I am someone that things tend to go wrong on the way to getting to the departure gate.
Will you have confirmed seat, i.e. you are booking direct with National Express. I once booked through Ryanair, (fare was the same), however I was told by the coach driver the Ryanair ticket is a standby.
I was lucky there was room on the coach, it was very early morning & not a busy day.
The coach before had been cancelled as the driver had not shown up.
On return back from Luton, I was cheesed off as had to wait for another coach. Arriving Luton airport, i.e. from flight, is usually very fast even with hold luggage. I would only in future book direct with National Express. By the way if you miss your National Express coach, I was told at the airport you get it stamped for either next coach or standby, but no idea how it works for stops along the way.
There are the odd tube/British Rail strikes this year in England, so best to check that with your date of travel does not coincide with one or those, if so, definitely get the earlier coach.
Personally I woudn't trust such a short arrival/gate-closing gap.
I've experiences traffic jams, non-arrival of scheduled coaches, once a long delay caused by a drunken student who'd removed his false leg as it was chaffing and then couldn't re-fit it in his panicked state (I kid you not, the driver had to call an ambulance to him in the end).
Take the earlier coach, read your book and have a spot of lunch before catching your plane.